Modeling and solving a Crew Assignment Problem in air transportation

Ecole Polytechnique de Tunisie, CORG-ROI, BP 743, 2078, La Marsa, Tunisia
European Journal of Operational Research (Impact Factor: 1.84). 11/2006; 175(1):187-209. DOI: 10.1016/j.ejor.2004.11.028
Source: DBLP

ABSTRACT A typical problem arising in airline crew management consists in optimally assigning the required crew members to each flight segment of a given time period, while complying with a variety of work regulations and collective agreements. This problem called the Crew Assignment Problem (CAP) is currently decomposed into two independent sub-problems which are modeled and solved sequentially: (a) the well-known Crew Pairing Problem followed by (b) the Working Schedules Construction Problem. In the first sub-problem, a set of legal minimum-cost pairings is constructed, covering all the planned flight segments. In the second sub-problem, pairings, rest periods, training periods, annual leaves, etc. are combined to form working schedules which are then assigned to crew members.In this paper, we present a new approach to the Crew Assignment Problem arising in the context of airline companies operating short and medium haul flights. Contrary to most previously published work on the subject, our approach is not based on the concept of crew-pairings, though it is capable of handling many of the constraints present in crew-pairing-based models. Moreover, contrary to crew-pairing-based approaches, one of its distinctive features is that it formulates and solves the two sub-problems (a) and (b) simultaneously for the technical crew members (pilots and officers) with specific constraints. We show how this problem can be formulated as a large scale integer linear program with a general structure combining different types of constraints and not exclusively partitioning or covering constraints as usually suggested in previous papers. We introduce then, a formulation enhancement phase where we replace a large number of binary exclusion constraints by stronger and less numerous ones: the clique constraints. Using data provided by the Tunisian airline company TunisAir, we demonstrate that thanks to this new formulation, the Crew Assignment Problem can be solved by currently available integer linear programming technology. Finally, we propose an efficient heuristic method based on a rounding strategy embedded in a partial tree search procedure.The implementation of these methods (both exact and heuristic ones) provides good solutions in reasonable computation times using CPLEX 6.0.2: guaranteed exact solutions are obtained for 60% of the test instances and solutions within 5% of the lower bound for the others.

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    ABSTRACT: Traditionally, the airline crew scheduling problem has been decomposed into a crew pairing problem and a crew assignment problem, both of which are solved sequentially. The first consists of generating a set of least-cost crew pairings (sequences of flights starting and ending at the same crew base) that cover all flights. The second aims at finding monthly schedules (sequences of pairings) for crew members that cover all pairings previously built. Pairing and schedule construction must respect all safety and collective agreement rules. In this paper, we focus on the pilot crew scheduling problem in a bidline context where anonymous schedules must be built for pilots and high fixed costs are considered to minimize the number of scheduled pilots. We propose a model that completely integrates the crew pairing and crew assignment problems, and we develop a combined column generation/dynamic constraint aggregation method for solving them. Computational results on real-life data show that integrating crew pairing and crew assignment can yield significant savings---on average, 3.37% on the total cost and 5.54% on the number of schedules for the 7 tested instances. The integrated approach, however, requires much higher computational times than the sequential approach.
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